Wytężenie Materiału w Stanach Podkrytycznych - Życzkowski, M. (Engineering Transactions, 1960)
Under the name of «exertion » of the material at a given point we shall understand the degree in which the physical state of the material approaches the dangerous state (elastic limit, yield point or strength). The equation of this state describes a limit surface (or hypersurface) in the space of exertion factors (stresses, temperature, etc.). This surface is assumed to be known. As a measure of exertion in subcritical states we assume as a rule the effective stress or the ratio of this stress to the dangerous limit for simple tension K,[Fig. 1, Eqs. (1.3) and (1.5)]. This measure, called by us elementary», implies the possibility of reaching the limit surface at one point, No, only, thus being valid for proportional loading. This measure is subjected to a critical analysis, a number of examples being given in which it leads to erroneous results. A general measure of exertion w is proposed. This is defined by the Eqs. (3.3) and (3.4) and Fig. 2. In this measure the probability various directions of the space of exertion factors of «motion» of a point in is taken into consideration.Thus it is not a one-valued function of exertion factors. Only such an approach a can have a practical importance, because the same state (prestressing of concrete, for instance) can be considered to be more or less distant from the dangerous state depending on whether tensile or compressive load is expected. In the particular case where the «motion» is likely to take place in only one direction of the space of stresses, the general formula (3.3) becomes the elementary one (1.5). In the measure w other factors, disregarded in the computation of the elementary measure w, are also taken into account, therefore the integrals appearing in the Eq. (3.4) and written using HADAMARD's notation concern a n-dimensional space. In the case where the probability depends on the direction in the space of exertion factors only and does not depend on the location of the point P. the general formula (3.3) takes the form (3.5) and, after iteration in spherical coordinates - the form (3.8). computing the exertion are given, by means In Secs. 4-6 several examples of  the general formula (3.3). The limit surface is assumed in the form of the HUBER-MISES-HENCKY cylinder (5.1) and the BURZYNSKI paraboloid (2.12). The exertion is also investigated in the case of two-point distribution of probability in a one-dimensional space of exertion factors (Sec. 6). The results obtained are represented by means of tables and graphs. The problem of invertigation of optimum initial stresses and minimum material exertion giving a certain appraisal of the advantages of using such stresses, is also treated.